22,458 research outputs found
Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes
In diffusion MRI (dMRI), a good sampling scheme is important for efficient
acquisition and robust reconstruction. Diffusion weighted signal is normally
acquired on single or multiple shells in q-space. Signal samples are typically
distributed uniformly on different shells to make them invariant to the
orientation of structures within tissue, or the laboratory coordinate frame.
The Electrostatic Energy Minimization (EEM) method, originally proposed for
single shell sampling scheme in dMRI, was recently generalized to multi-shell
schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the
Human Connectome Project (HCP). However, EEM does not directly address the goal
of optimal sampling, i.e., achieving large angular separation between sampling
points. In this paper, we propose a more natural formulation, called Spherical
Code (SC), to directly maximize the minimal angle between different samples in
single or multiple shells. We consider not only continuous problems to design
single or multiple shell sampling schemes, but also discrete problems to
uniformly extract sub-sampled schemes from an existing single or multiple shell
scheme, and to order samples in an existing scheme. We propose five algorithms
to solve the above problems, including an incremental SC (ISC), a sophisticated
greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt
greedy method, a Mixed Integer Linear Programming (MILP) method, and a
Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is
the first work to use the SC formulation for single or multiple shell sampling
schemes in dMRI. Experimental results indicate that SC methods obtain larger
angular separation and better rotational invariance than the state-of-the-art
EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been
released in dmritool
https://diffusionmritool.github.io/tutorial_qspacesampling.htm
Distributed Unmixing of Hyperspectral Data With Sparsity Constraint
Spectral unmixing (SU) is a data processing problem in hyperspectral remote
sensing. The significant challenge in the SU problem is how to identify
endmembers and their weights, accurately. For estimation of signature and
fractional abundance matrices in a blind problem, nonnegative matrix
factorization (NMF) and its developments are used widely in the SU problem. One
of the constraints which was added to NMF is sparsity constraint that was
regularized by L 1/2 norm. In this paper, a new algorithm based on distributed
optimization has been used for spectral unmixing. In the proposed algorithm, a
network including single-node clusters has been employed. Each pixel in
hyperspectral images considered as a node in this network. The distributed
unmixing with sparsity constraint has been optimized with diffusion LMS
strategy, and then the update equations for fractional abundance and signature
matrices are obtained. Simulation results based on defined performance metrics,
illustrate advantage of the proposed algorithm in spectral unmixing of
hyperspectral data compared with other methods. The results show that the AAD
and SAD of the proposed approach are improved respectively about 6 and 27
percent toward distributed unmixing in SNR=25dB.Comment: 6 pages, conference pape
Distributed Learning for Stochastic Generalized Nash Equilibrium Problems
This work examines a stochastic formulation of the generalized Nash
equilibrium problem (GNEP) where agents are subject to randomness in the
environment of unknown statistical distribution. We focus on fully-distributed
online learning by agents and employ penalized individual cost functions to
deal with coupled constraints. Three stochastic gradient strategies are
developed with constant step-sizes. We allow the agents to use heterogeneous
step-sizes and show that the penalty solution is able to approach the Nash
equilibrium in a stable manner within , for small step-size
value and sufficiently large penalty parameters. The operation
of the algorithm is illustrated by considering the network Cournot competition
problem
Distributed Coupled Multi-Agent Stochastic Optimization
This work develops effective distributed strategies for the solution of
constrained multi-agent stochastic optimization problems with coupled
parameters across the agents. In this formulation, each agent is influenced by
only a subset of the entries of a global parameter vector or model, and is
subject to convex constraints that are only known locally. Problems of this
type arise in several applications, most notably in disease propagation models,
minimum-cost flow problems, distributed control formulations, and distributed
power system monitoring. This work focuses on stochastic settings, where a
stochastic risk function is associated with each agent and the objective is to
seek the minimizer of the aggregate sum of all risks subject to a set of
constraints. Agents are not aware of the statistical distribution of the data
and, therefore, can only rely on stochastic approximations in their learning
strategies. We derive an effective distributed learning strategy that is able
to track drifts in the underlying parameter model. A detailed performance and
stability analysis is carried out showing that the resulting coupled diffusion
strategy converges at a linear rate to an neighborhood of the true
penalized optimizer
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